R Notebook
ANPR-Based Automatic Abnormal Traffic Flow Detection
The following page is made for anpr flow data exploration purpose. The data is taken from github repo https://github.com/ppintosilva/congestion18tynewear/blob/master/data-raw/events.R. We’ll set-up caching for this notebook given how computationally expensive some of the code we will write can get.
knitr::opts_chunk$set(cache=TRUE)
options(scipen=9999)
rm(list=ls())Importing libraries
library(tidyverse)
library(lubridate)
library(sf)
library(maotai)
library(ggpubr)Define corridor level
corridor_levels = c(1, 2, 3)Create flow dataframe for 2-3 camera pairs
flows <- read_csv(
file = "data/corridor_A184_WEST_3cameras.csv",
col_names = TRUE,
col_types = list(
o = col_integer(),
d = col_integer(),
t = col_datetime(),
flow = col_integer(),
mean_speed = col_double()
)
) %>%
mutate(o = factor(o, levels = corridor_levels),
d = factor(d, levels = corridor_levels))Get the flow data on weekday across 2-3 pair
flows_23_weekday <-
flows %>%
filter(o == 2 & d == 3) %>%
filter(wday(t, week_start = 1) < 6)Daily flow for corridor 2-3
p_daily_flow <-
flows_23_weekday %>%
ggplot() +
geom_line(
aes(x = hms::as_hms(t), y = flow, group = as_date(t)),
alpha = .5
) +
scale_x_time(
name = "Time",
breaks = hms::hms(hours = seq(2, 22, 4)),
labels = scales::label_time("%Hh")
) +
theme_bw()
p_daily_flow
Flow Descriptive Stats
flows_23_weekday %>%
group_by(as_date(t)) %>%
summary()## o d t flow
## 1: 0 1: 0 Min. :2018-01-01 00:00:00 Min. : 0.00
## 2:24961 2: 0 1st Qu.:2018-04-02 00:00:00 1st Qu.: 7.00
## 3: 0 3:24961 Median :2018-07-02 00:00:00 Median : 48.00
## Mean :2018-07-01 00:03:03 Mean : 63.88
## 3rd Qu.:2018-10-01 00:00:00 3rd Qu.: 93.00
## Max. :2018-12-31 00:00:00 Max. :367.00
##
## mean_speed as_date(t)
## Min. : 3.007 Min. :2018-01-01
## 1st Qu.:30.195 1st Qu.:2018-04-02
## Median :34.933 Median :2018-07-02
## Mean :34.054 Mean :2018-06-30
## 3rd Qu.:40.890 3rd Qu.:2018-10-01
## Max. :65.651 Max. :2018-12-31
## NA's :5333p_daily_mean_speed <-
flows_23_weekday %>%
ggplot() +
geom_line(
aes(x = hms::as_hms(t), y = mean_speed, group = as_date(t)),
alpha = .5
) +
scale_x_time(
name = "Time",
breaks = hms::hms(hours = seq(2, 22, 4)),
labels = scales::label_time("%Hh")
) +
theme_classic()
p_daily_mean_speed## Warning: Removed 4312 row(s) containing missing values (geom_path).
sum(is.na(flows_23_weekday$mean_speed))## [1] 5333sum(is.na(flows_23_weekday$flow))## [1] 0Classify daily flow based on threshold
expected_flow <-
flows_23_weekday %>%
mutate(time = hms::as_hms(t)) %>%
group_by(o,d,time) %>%
summarise(
median_flow = median(flow)
)deviation_flow <-
flows_23_weekday %>%
mutate(time = hms::as_hms(t)) %>%
group_by(o, d, time) %>%
summarise(
mad_flow = mad(flow)
)flow_with_expected <-
flows_23_weekday %>%
mutate(time = hms::as_hms(t)) %>%
inner_join(expected_flow, by = c("o", "d", "time"))flow_with_expected <-
flow_with_expected %>%
mutate(har_mean_speed = mean_speed - (var(mean_speed, na.rm = TRUE)/mean_speed))cor.test(flow_with_expected$flow, flow_with_expected$har_mean_speed, method = "pearson")##
## Pearson's product-moment correlation
##
## data: flow_with_expected$flow and flow_with_expected$har_mean_speed
## t = -89.549, df = 19626, p-value < 0.00000000000000022
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.5484381 -0.5285732
## sample estimates:
## cor
## -0.5385805cor.test(flow_with_expected$flow, flow_with_expected$mean_speed, method = "pearson")##
## Pearson's product-moment correlation
##
## data: flow_with_expected$flow and flow_with_expected$mean_speed
## t = -94.53, df = 19626, p-value < 0.00000000000000022
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.5688786 -0.5496514
## sample estimates:
## cor
## -0.5593403p_median <- ggplot(flow_with_expected) +
geom_line(aes(x = time, y = flow, group = date(t)), color = "grey") +
geom_line(aes(x = time, y = median_flow), color = "black") +
scale_x_time(
name = "Time",
breaks = hms::hms(hours = seq(2, 24, 4)),
labels = scales::label_time("%H:%M")
) +
theme_bw()
p_median
flow_with_expected %>%
filter(as_date(t) == "2018-10-02") %>%
mutate(flow_diff = abs(flow - median_flow)) %>%
mutate(outlier = ifelse(flow_diff > 40, TRUE, FALSE)) %>%
ggplot() +
geom_line(aes(x = time, y = flow_diff)) +
geom_hline(yintercept = 40, color = "red") +
theme_bw()
Clustering flow data using EP-MEANS
p_daily_ecdf <-
flow_with_expected %>%
ggplot() +
stat_ecdf(
aes(x = flow, group = as_date(t)),
alpha = .7
) +
xlab("Vehicle count per time period (15min)") +
ylab("Cumulative probability") +
theme_bw()
p_daily_ecdf
EP Means
Create flows_ecd23 (give index based on date and o-d pair)
flows_ecd23 <-
flow_with_expected %>%
mutate(dayt = as_date(t)) %>%
group_by(o, d, dayt) %>%
summarise(ecd = list(ecdf(flow))) %>%
group_by(dayt) %>%
mutate(date_index = group_indices()) %>%
group_by(o, d) %>%
mutate(group_id = group_indices())
head(flows_ecd23)## # A tibble: 6 x 6
## # Groups: o, d [1]
## o d dayt ecd date_index group_id
## <fct> <fct> <date> <list> <int> <int>
## 1 2 3 2018-01-01 <ecdf> 1 1
## 2 2 3 2018-01-02 <ecdf> 2 1
## 3 2 3 2018-01-03 <ecdf> 3 1
## 4 2 3 2018-01-04 <ecdf> 4 1
## 5 2 3 2018-01-05 <ecdf> 5 1
## 6 2 3 2018-01-08 <ecdf> 6 1flow_with_expected %>%
filter(as_date(t) == c("2018-04-02", "2018-01-01"))## Warning in `==.default`(as_date(t), c("2018-04-02", "2018-01-01")): longer
## object length is not a multiple of shorter object length## # A tibble: 96 x 8
## o d t flow mean_speed time median_flow
## <fct> <fct> <dttm> <int> <dbl> <tim> <dbl>
## 1 2 3 2018-01-01 00:15:00 40 40.5 00:15 20
## 2 2 3 2018-01-01 00:45:00 46 38.6 00:45 14
## 3 2 3 2018-01-01 01:15:00 38 41.0 01:15 14
## 4 2 3 2018-01-01 01:45:00 56 40.1 01:45 11
## 5 2 3 2018-01-01 02:15:00 42 37.0 02:15 14
## 6 2 3 2018-01-01 02:45:00 45 43.7 02:45 15
## 7 2 3 2018-01-01 03:15:00 34 45.7 03:15 21.5
## 8 2 3 2018-01-01 03:45:00 37 39.8 03:45 24
## 9 2 3 2018-01-01 04:15:00 41 40.0 04:15 31
## 10 2 3 2018-01-01 04:45:00 28 40.5 04:45 30
## # … with 86 more rows, and 1 more variable: har_mean_speed <dbl>p_01_ecdf <-
flow_with_expected %>%
filter(as_date(t) == c("2018-04-02", "2018-01-02")) %>%
ggplot() +
stat_ecdf(
aes(x = flow, group = as_date(t)),
alpha = .7
) +
theme_bw() +
xlab("Vehicle count per time period (15min)") +
ylab("Cumulative probability") ## Warning in `==.default`(as_date(t), c("2018-04-02", "2018-01-02")): longer
## object length is not a multiple of shorter object lengthp_01_ecdf
Apply EP Means to flows_ecd23 with number of cluster == 2
epout_k2 <- flows_ecd23 %>%
group_map(~ { maotai::epmeans(.x$ecd, k = 2) })
epout_k2## [[1]]
## [[1]]$cluster
## [1] 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [38] 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [75] 2 2 2 2 2 2 1 2 1 1 1 1 2 1 2 1 2 2 1 2 1 2 2 1 2 2 2 1 2 2 1 2 2 2 2 2 2
## [112] 2 2 2 1 2 2 2 1 1 2 1 1 2 2 2 2 2 2 2 2 2 2 2 2 1 2 1 1 2 2 2 2 2 1 2 2 2
## [149] 2 2 2 2 2 2 2 1 2 2 2 2 1 1 1 1 1 2 1 2 1 1 2 2 1 2 2 1 1 1 1 1 1 2 2 1 1
## [186] 2 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [223] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1
## [260] 1 2
##
## [[1]]$centers
## [[1]]$centers[[1]]
## Empirical CDF
## Call: stats::ecdf(as.vector(tmpcpp[k, ]))
## x[1:1000] = 3.8972, 3.9929, 4.0887, ..., 264.4, 265.39
##
## [[1]]$centers[[2]]
## Empirical CDF
## Call: stats::ecdf(as.vector(tmpcpp[k, ]))
## x[1:1000] = 1.08, 1.1074, 1.1348, ..., 98.821, 99.511Create daily cluster dataframe
daily_cluster_ids <- epout_k2 %>%
lapply(function(x) x$cluster %>%
enframe(name = "date_index", value = "cluster")) %>%
enframe(name = "group_id", value = "value") %>%
unnest(value)
head(daily_cluster_ids)## # A tibble: 6 x 3
## group_id date_index cluster
## <int> <int> <int>
## 1 1 1 2
## 2 1 2 1
## 3 1 3 1
## 4 1 4 1
## 5 1 5 1
## 6 1 6 1Calculate 80% quantile in flow data
flow_80quantiles <- flows_23_weekday %>%
group_by(o,d) %>%
summarise(quantile80 = quantile(flow, 0.8))Create centroids
Assume that the centroids which corresponds to “typical” traffic is the one who carries more traffic most of the times, i.e. will have lower cummulative probability of carrying less or equal than 80th percentile of the flow
ecd_centroids_k2 <- epout_k2 %>%
lapply(function(x) x$centers %>% enframe(name = "cluster", value = "centroid")) %>%
enframe(name = "group_id", value = "value") %>%
unnest(value) %>%
inner_join(flows_ecd23 %>% distinct(o,d) %>% mutate(group_id = group_indices()),
by = "group_id") %>%
select(-group_id) %>%
select(o, d, cluster, centroid) %>%
# label which centroid is typical and atypical
# for a high quantile (e.g. 80% quantile)
inner_join(flow_80quantiles, by = c("o", "d")) %>%
group_by(o, d, cluster) %>%
mutate(prob80 = centroid[[1]](quantile80)) %>%
group_by(o, d) %>%
arrange(prob80) %>%
mutate(cluster_label = c("typical", "atypical")) %>%
mutate(cluster_label = factor(cluster_label)) %>%
arrange(o, d, prob80)max_flow <- max(flows$flow)
npoints = 500ecd_centroids_k2_xy <-
ecd_centroids_k2 %>%
group_by(o, d, cluster) %>%
group_modify(~{
tibble(
cluster_label = .$cluster_label,
ecd_x = seq(0, max_flow, length.out = npoints)
) %>%
mutate(ecd_y = .x$centroid[[1]](ecd_x))
})od_day_labels <- flows_ecd23 %>%
inner_join(daily_cluster_ids, by = c("group_id", "date_index")) %>%
select(-c(date_index, group_id, ecd)) %>%
inner_join(
ecd_centroids_k2 %>% distinct(o, d, cluster, cluster_label),
by = c("o", "d", "cluster")
)flows_23_labelled <-
flows_23_weekday %>%
mutate(dayt = as_date(t)) %>%
mutate(month = month(t)) %>%
inner_join(od_day_labels %>% select (-cluster), by = c("o", "d", "dayt"))flows_23_labelled[flows_23_labelled$month == 5,]## # A tibble: 2,208 x 8
## o d t flow mean_speed dayt month
## <fct> <fct> <dttm> <int> <dbl> <date> <dbl>
## 1 2 3 2018-05-01 00:00:00 14 45.2 2018-05-01 5
## 2 2 3 2018-05-01 00:15:00 8 45.6 2018-05-01 5
## 3 2 3 2018-05-01 00:30:00 6 38.1 2018-05-01 5
## 4 2 3 2018-05-01 00:45:00 9 50.7 2018-05-01 5
## 5 2 3 2018-05-01 01:00:00 34 48.0 2018-05-01 5
## 6 2 3 2018-05-01 01:15:00 18 37.8 2018-05-01 5
## 7 2 3 2018-05-01 01:30:00 14 43.9 2018-05-01 5
## 8 2 3 2018-05-01 01:45:00 12 42.2 2018-05-01 5
## 9 2 3 2018-05-01 02:00:00 18 41.1 2018-05-01 5
## 10 2 3 2018-05-01 02:15:00 17 45.1 2018-05-01 5
## # … with 2,198 more rows, and 1 more variable: cluster_label <fct>p_all_clustered_ecdf <-
flows_23_labelled %>%
mutate(tday = factor(as_date(t))) %>%
ggplot() +
stat_ecdf(
aes(x = flow, group = tday, colour = cluster_label),
alpha = .6
) +
geom_line(
data = ecd_centroids_k2_xy,
mapping = aes(x = ecd_x, y = ecd_y, colour = cluster_label),
size = 2
) +
geom_vline(
xintercept = ecd_centroids_k2$quantile80,
linetype = "dotted",
size = 1.0
) +
geom_hline(
yintercept = ecd_centroids_k2$prob80,
linetype = "dashed",
size = 1.0
) +
scale_color_grey(name = "Daily behaviour") +
theme_bw() +
xlab("Vehicle count per time period (15min)") +
ylab("Cumulative probability")
p_all_clustered_ecdf
p_test <-
flows_23_labelled %>%
mutate(tday = factor(as_date(t))) %>%
ggplot() +
stat_ecdf(
aes(x = flow, group = tday, colour = cluster_label),
alpha = .6
) +
geom_line(
data = ecd_centroids_k2_xy,
mapping = aes(x = ecd_x, y = ecd_y, colour = cluster_label),
size = 2
)
p_test
p_daily_flow_labelled <-
flows_23_labelled %>%
ggplot() +
geom_line(
aes(x = hms::as_hms(t), y = flow, group = as_date(t)), alpha = .5
) +
scale_x_time(
name = "Time",
breaks = hms::hms(hours = seq(2,22,4)),
labels = scales::label_time("%Hh")
) +
facet_wrap(~cluster_label) +
theme_bw()
p_daily_flow_labelled
p_daily_speed_labelled <-
flows_23_labelled %>%
ggplot() +
geom_line(
aes(x = hms::as_hms(t), y = mean_speed, group = as_date(t)), alpha = .5
) +
scale_x_time(
name = "Time",
breaks = hms::hms(hours = seq(2,22,4)),
labels = scales::label_time("%Hh")
) +
facet_wrap(~cluster_label) +
theme_bw()
p_daily_speed_labelled## Warning: Removed 4312 row(s) containing missing values (geom_path).
Check correlation between labelled flow vs speed
x <- flows_23_labelled %>% filter(flow, cluster_label == "typical")
y <- flows_23_labelled %>% filter(mean_speed, cluster_label == "typical")
a <- flows_23_labelled %>% filter(flow, cluster_label == "atypical")
b <- flows_23_labelled %>% filter(mean_speed, cluster_label == "atypical")
cor.test(x$flow, y$mean_speed, method = "pearson")##
## Pearson's product-moment correlation
##
## data: x$flow and y$mean_speed
## t = -92.894, df = 13398, p-value < 0.00000000000000022
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.6360924 -0.6154927
## sample estimates:
## cor
## -0.6259017cor.test(a$flow, b$mean_speed, method = "pearson")##
## Pearson's product-moment correlation
##
## data: a$flow and b$mean_speed
## t = -22.736, df = 6226, p-value < 0.00000000000000022
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.299654 -0.253787
## sample estimates:
## cor
## -0.2768782Estimate function for each classes
flows_23_atypical <- flows_23_labelled[flows_23_labelled$cluster_label == 'atypical',]
flows_23_typical <- flows_23_labelled[flows_23_labelled$cluster_label == 'typical',]Mean for atypical phenomenon in road segment 2-3
flows_23_atypical$time <- hms::as_hms(flows_23_atypical$t)
flows_23_atypical_mean <- aggregate(flows_23_atypical[,4], list(as.character(flows_23_atypical$time)), mean)Mean for typical phenomenon in road segment 2-3
flows_23_typical$time <- hms::as_hms(flows_23_typical$t)
flows_23_typical_mean <- aggregate(flows_23_typical[,4], list(as.character(flows_23_typical$time)), mean)Plot typical vs atypical
flows_23_mean_combined <- data.frame("t"=flows_23_atypical_mean$Group.1, "flow_atypical"=flows_23_atypical_mean$flow, "flow_typical"=flows_23_typical_mean$flow)
# flows_23_mean_combined$t <- as.character(flows_23_mean_combined$t)
# flows_23_mean_combined$t <- chron::as.times(flows_23_mean_combined$t)
flows_23_mean_combined$t <- as.POSIXct(flows_23_mean_combined$t, format = "%H:%M:%S")flow_23_mean_compare <- ggplot(flows_23_mean_combined, aes(x = t)) +
geom_line(aes(y = flow_atypical), colour = "red") +
geom_line(aes(y = flow_typical), colour= "green") +
scale_x_datetime(date_labels = "%H:%M") +
theme_bw()
flow_23_mean_compare
Cluster the flows based on ep-typical median value
expected_flow_typ <-
flows_23_typical %>%
mutate(time = hms::as_hms(t)) %>%
#filter(!month(t) %in% c(3,4)) %>%
group_by(o,d,time) %>%
summarise(
median_flow_typ = median(flow)
)deviation_flow_typ <-
flows_23_typical %>%
mutate(time = hms::as_hms(t)) %>%
group_by(o, d, time) %>%
summarise(
mad_flow_typ = mad(flow)
)flow_with_expected <- inner_join(flow_with_expected, expected_flow_typ, by = c("o", "d", "time"))expected_flow_atyp <-
flows_23_atypical %>%
mutate(time = hms::as_hms(t)) %>%
#filter(!month(t) %in% c(3,4)) %>%
group_by(o,d,time) %>%
summarise(
median_flow_atyp = median(flow)
)expected_flow_atyp_real <-
flows_23_atypical %>%
filter(flow != 0) %>%
group_by(o, d, time) %>%
summarise(
median_flow_atyp_real = median(flow)
)deviation_flow_atyp <-
flows_23_atypical %>%
mutate(time = hms::as_hms(t)) %>%
group_by(o, d, time) %>%
summarise(
mad_flow_atyp = mad(flow)
)flow_with_expected <- inner_join(flow_with_expected, expected_flow_atyp, by = c("o", "d", "time"))flow_with_expected <- inner_join(flow_with_expected, expected_flow_atyp_real, by = c("o", "d", "time"))p_median_ep <- ggplot(flow_with_expected) +
geom_line(aes(x = time, y = flow, group = date(t)), color = "grey") +
geom_line(aes(x = time, y = median_flow_typ), color = "black") +
scale_x_time(
name = "Time",
breaks = hms::hms(hours = seq(2, 24, 4)),
labels = scales::label_time("%H:%M")
) +
theme_bw()
p_median_ep
p_median_ep_atyp <- ggplot(flow_with_expected) +
geom_line(aes(x = time, y = flow, group = date(t)), color = "grey") +
geom_line(aes(x = time, y = median_flow_atyp), color = "black") +
scale_x_time(
name = "Time",
breaks = hms::hms(hours = seq(2, 24, 4)),
labels = scales::label_time("%H:%M")
) +
theme_bw()
p_median_ep
p_median_comp <-
ggplot(flow_with_expected) +
geom_line(
aes(x = time, y = flow, group = date(t)),
color = "grey"
) +
geom_line(
aes(x = time, y = median_flow, group = date(t)),
linetype = "solid"
) +
geom_line(
aes(x = time, y = median_flow_typ, group = date(t)),
linetype = "dotted"
) +
geom_line(
aes(x = time, y = median_flow_atyp, group = date(t)),
linetype = "dashed"
) +
theme_bw()
p_median_comp
p_atypical_comp <-
ggplot(flow_with_expected) +
geom_line(
aes(
x = time,
y = median_flow_atyp
),
linetype = "solid"
) +
geom_line(
aes(
x = time,
y = median_flow_atyp_real
),
linetype = "dashed"
) +
theme(legend.position = "top") +
xlab("Time") +
ylab("Atypical Median") +
theme_bw()
p_atypical_comp
ggarrange(p_median, p_median_ep,
ncol = 3, nrow = 1)
Variance comparison
ggplot() +
geom_line(
data = deviation_flow,
aes(x = time, y = mad_flow),
linetype = "solid"
) +
geom_line(
data = deviation_flow_typ,
aes(x = time, y = mad_flow_typ),
linetype = "dotted"
) +
geom_line(
data = deviation_flow_atyp,
aes(x = time, y = mad_flow_atyp),
linetype = "dashed"
) +
theme_bw()
Flow-speed plot
flows_23_typical %>% filter(month == 6) %>%
ggplot() +
geom_point(aes(
x = mean_speed,
y = flow
)) +
theme_bw()## Warning: Removed 1 rows containing missing values (geom_point).
Quadratic function fitting
quad_fit <- lm(formula = flow ~ poly(mean_speed, 2, raw = TRUE), data = flows_23_weekday)
summary(quad_fit)##
## Call:
## lm(formula = flow ~ poly(mean_speed, 2, raw = TRUE), data = flows_23_weekday)
##
## Residuals:
## Min 1Q Median 3Q Max
## -170.800 -29.449 -3.577 24.347 199.498
##
## Coefficients:
## Estimate Std. Error t value
## (Intercept) 174.295536 2.855249 61.044
## poly(mean_speed, 2, raw = TRUE)1 -0.659595 0.194332 -3.394
## poly(mean_speed, 2, raw = TRUE)2 -0.056618 0.003224 -17.561
## Pr(>|t|)
## (Intercept) < 0.0000000000000002 ***
## poly(mean_speed, 2, raw = TRUE)1 0.00069 ***
## poly(mean_speed, 2, raw = TRUE)2 < 0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 54.85 on 19625 degrees of freedom
## (5333 observations deleted due to missingness)
## Multiple R-squared: 0.3235, Adjusted R-squared: 0.3234
## F-statistic: 4692 on 2 and 19625 DF, p-value: < 0.00000000000000022quad_eq <- quad_fit$coefficient[3]*flows_23_weekday$mean_speed^2 + quad_fit$coefficient[2]*flows_23_weekday$mean_speed + quad_fit$coefficient[1]
quad_eq <- as.data.frame(quad_eq)quad_fit_plot <- flows_23_weekday %>%
select(flow, mean_speed) %>%
cbind(quad_eq)
quad_fit_plot## flow mean_speed quad_eq
## 1 22 38.416267 65.39886695
## 2 40 40.495816 54.73609326
## 3 58 38.196401 66.49759575
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## 1590 91 32.488577 93.10542619
## 1591 86 32.681970 92.26428040
## 1592 96 34.539445 83.96964493
## 1593 107 34.116004 85.89491982
## 1594 122 32.531610 92.91862435
## 1595 118 34.473190 84.27223152
## 1596 91 34.764586 82.93772116
## 1597 114 36.051452 76.92926366
## 1598 114 34.473122 84.27253883
## 1599 141 32.716339 92.11435209
## 1600 147 34.375501 84.71746497
## 1601 134 33.173793 90.10605077
## 1602 160 35.731590 78.44023290
## 1603 181 30.947416 99.65724048
## 1604 196 32.153444 94.55303562
## 1605 194 28.485316 109.56611501
## 1606 218 21.869887 132.79030061
## 1607 228 20.181621 137.92342442
## 1608 224 20.961738 135.59161304
## 1609 233 27.065773 114.96717851
## 1610 222 29.095409 107.17472859
## 1611 199 31.080959 99.10016407
## 1612 173 31.257792 98.35939344
## 1613 162 33.043073 90.68235386
## 1614 105 35.240755 80.73631697
## 1615 96 36.533152 74.63194400
## 1616 102 35.938952 77.46201634
## 1617 87 37.101129 71.88939459
## 1618 77 38.025818 67.34626885
## 1619 53 37.116616 71.81410127
## 1620 77 36.866117 73.02861193
## 1621 69 38.411566 65.42241523
## 1622 80 37.607798 69.41204933
## 1623 79 37.140314 71.69883971
## 1624 68 36.984116 72.45739484
## 1625 66 40.041439 57.10769514
## 1626 67 38.533611 64.81022929
## 1627 47 34.855404 82.51983863
## 1628 46 37.985413 67.54680761
## 1629 58 39.242756 61.21972739
## 1630 58 43.547067 38.20459338
## 1631 53 42.779717 42.46127800
## 1632 30 38.026567 67.34255071
## 1633 16 34.586804 83.75305639
## 1634 23 41.239944 50.80165292
## 1635 15 41.949696 46.99054868
## 1636 15 40.945778 52.36449476
## 1637 24 41.332400 50.30842882
## 1638 19 42.473780 44.13979960
## 1639 16 41.453489 49.66099347
## 1640 11 45.931142 24.55414663
## 1641 34 46.713214 19.93606200
## 1642 19 44.101551 35.08723626
## 1643 14 46.719090 19.90110260
## 1644 7 36.923202 72.75246907
## 1645 9 44.524262 32.68732820
## 1646 11 44.975885 30.10092141
## 1647 14 42.335275 44.89621667
## 1648 9 39.641811 59.17421519
## 1649 12 36.159435 76.41655726
## 1650 16 44.267590 34.14697364
## 1651 30 41.796763 47.81656223
## 1652 21 41.387369 50.01473192
## 1653 20 43.978499 35.78205001
## 1654 44 44.119923 34.98335096
## 1655 61 39.648506 59.13974232
## 1656 90 41.692245 48.37955830
## 1657 73 40.189862 56.33557904
## 1658 158 34.487228 84.20816042
## 1659 245 24.422539 124.41611659
## 1660 266 19.219522 140.70428774
## 1661 270 15.196542 151.19688673
## 1662 286 10.168165 161.73483420
## 1663 310 8.256234 164.99037362
## 1664 330 6.748120 167.26628679
## 1665 359 5.925722 168.39886300
## 1666 332 5.398221 169.08500148
## 1667 303 5.234851 169.29111248
## 1668 282 5.549227 168.89180269
## 1669 297 6.043726 168.24105885
## 1670 311 7.175387 166.64763928
## 1671 237 8.379475 164.79300620
## 1672 186 13.337585 155.42627828
## 1673 172 23.965148 125.97088372
## 1674 124 30.206749 102.71028844
## 1675 90 28.158831 110.82852515
## 1676 20 25.005358 122.40066406
## 1677 3 3.898405 170.86371149
## 1678 9 31.573598 97.02764112
## 1679 61 34.104161 85.94847513
## 1680 78 32.406911 93.45935467
## 1681 88 31.277370 98.27716057
## 1682 96 30.882663 99.92663119
## 1683 113 28.864870 108.08332796
## 1684 104 28.425194 109.79949294
## 1685 111 31.787302 96.12004662
## 1686 108 30.535412 101.36319636
## 1687 123 31.198779 98.60699610
## 1688 96 32.015394 95.14564599
## 1689 92 31.149037 98.81539801
## 1690 109 31.984848 95.27647816
## 1691 109 33.832602 87.17213322
## 1692 122 34.723767 83.12523923
## 1693 110 33.134593 90.27907577
## 1694 130 33.068425 90.57073424
## 1695 134 34.321286 84.96409108
## 1696 165 32.720799 92.09488433
## 1697 172 31.364225 97.91182782
## 1698 189 30.910255 99.81189892
## 1699 218 27.991379 111.47132435
## 1700 235 29.191235 106.79528979
## 1701 248 24.220043 125.10736381
## 1702 207 21.014310 135.43199392
## 1703 228 22.413174 131.06981259
## 1704 238 28.392739 109.92530369
## 1705 216 32.561331 92.78948516
## 1706 237 30.293347 102.35653525
## 1707 178 33.590731 88.25498452
## 1708 150 32.995157 90.89311227
## 1709 143 36.422476 75.16210595
## 1710 138 36.895169 72.88812206
## 1711 119 35.431956 79.84513715
## 1712 128 35.604943 79.03529026
## 1713 106 34.880538 82.40402181
## 1714 91 38.149550 66.73101117
## 1715 80 36.577112 74.42098128
## 1716 89 37.019088 72.28779522
## 1717 68 38.201288 66.47323421
## 1718 77 36.801135 73.34250467
## 1719 74 37.336044 70.74440115
## 1720 50 38.784404 63.54693584
## 1721 63 39.568192 59.55293706
## 1722 57 40.912853 52.53881111
## 1723 51 41.287935 50.54575538
## 1724 40 41.816836 47.70829452
## 1725 53 42.216873 45.54112505
## 1726 59 41.079138 51.65719684
## 1727 68 39.021082 62.34821204
## 1728 30 39.985302 57.39907860
## 1729 22 35.130958 81.24620169
## 1730 34 39.690573 58.92303305
## 1731 23 43.724382 37.21149966
## 1732 13 42.710076 42.84429237
## 1733 17 39.612852 59.32326464
## 1734 19 40.424388 55.11045593
## 1735 22 39.500205 59.90213810
## 1736 15 46.715955 19.91975399
## 1737 13 44.928755 30.37190885
## 1738 14 43.919126 36.11669011
## 1739 19 41.655936 48.57485096
## 1740 6 31.191724 98.63657167
## 1741 7 37.835178 68.29083594
## 1742 10 45.613494 26.41006430
## 1743 17 41.291945 50.52436379
## 1744 18 41.924951 47.12437557
## 1745 15 39.087574 62.01030023
## 1746 19 38.821312 63.36042320
## 1747 28 40.565371 54.37098992
## 1748 22 41.657582 48.56599656
## 1749 28 40.555093 54.42497831
## 1750 51 39.685946 58.94687717
## 1751 58 41.977302 46.84115808
## 1752 72 41.435912 49.75507646
## 1753 72 40.380904 55.33807987
## 1754 150 35.312189 80.40385251
## 1755 215 31.915729 95.57213378
## 1756 235 25.731896 119.83435694
## 1757 248 22.755075 129.96993719
## 1758 259 18.360411 143.09888406
## 1759 253 12.940374 156.27925038
## 1760 265 9.783857 162.42245354
## 1761 277 8.963653 163.83406077
## 1762 253 8.241708 165.01352325
## 1763 164 7.935277 165.49630598
## 1764 53 8.091508 165.25149188
## 1765 3 4.644680 170.01050417
## 1766 25 14.278237 153.33506873
## 1767 28 14.964302 151.74665552
## 1768 3 16.321337 148.44780228
## 1769 37 29.642517 104.99438262
## 1770 85 29.776884 104.45371464
## 1771 19 24.633997 123.68931801
## 1772 0 NA NA
## 1773 20 33.194747 90.01349209
## 1774 33 31.088796 99.06740931
## 1775 59 32.325844 93.80994336
## 1776 61 33.642651 88.02309720
## 1777 72 29.994420 103.57405751
## 1778 97 31.383324 97.83137850
## 1779 72 30.492171 101.54112989
## 1780 90 30.800783 100.26659717
## 1781 103 33.095935 90.44953492
## 1782 104 31.806124 96.03986505
## 1783 100 31.950728 95.42249481
## 1784 107 34.445742 84.39743679
## 1785 132 32.474624 93.16594947
## 1786 155 31.203742 98.58618816
## 1787 121 33.783023 87.39463483
## 1788 135 35.448484 79.76790774
## 1789 157 35.746110 78.37189340
## 1790 142 35.163702 81.09428365
## 1791 150 34.816833 82.69742867
## 1792 173 32.906490 91.28243442
## 1793 178 32.264562 94.07446903
## 1794 205 34.370916 84.73833641
## 1795 230 29.893727 103.98189930
## 1796 230 27.569379 113.07717973
## 1797 243 25.316285 121.30971274
## 1798 220 20.711756 136.34632463
## 1799 230 24.448559 124.32695624
## 1800 220 31.411999 97.71051565
## 1801 202 29.417835 105.89389018
## 1802 221 30.145041 102.96184823
## 1803 241 29.283551 106.42876435
## 1804 215 31.575279 97.02052228
## 1805 141 35.700439 78.58676377
## 1806 142 35.238124 80.74855202
## 1807 152 34.559686 83.87710762
## 1808 120 35.005282 81.82815503
## 1809 72 38.353894 65.71111658
## 1810 109 36.054255 76.91597230
## 1811 92 37.569459 69.60052486
## 1812 77 36.686767 73.89379679
## 1813 81 39.102671 61.93351108
## 1814 98 39.416644 60.33061417
## 1815 67 41.523310 49.28692255
## 1816 60 41.255098 50.72087754
## 1817 76 38.225603 66.35198077
## 1818 66 37.889081 68.02417774
## 1819 67 40.611584 54.12810840
## 1820 54 37.327891 70.78424110
## 1821 61 39.987539 57.38747147
## 1822 52 40.513843 54.64152305
## 1823 70 38.876856 63.07944058
## 1824 37 37.812480 68.40302010
## 1825 19 36.407815 75.23223002
## 1826 25 40.283416 55.84761588
## 1827 18 41.495611 49.43538935
## 1828 26 42.897486 41.81231841
## 1829 42 45.092445 29.42963910
## 1830 26 45.551290 26.77216215
## 1831 18 41.792028 47.84209512
## 1832 11 42.680022 43.00941804
## 1833 16 40.270837 55.91328352
## 1834 9 47.330140 16.24428014
## 1835 19 42.248180 45.37076098
## 1836 16 43.006231 41.21168430
## 1837 10 46.516964 21.10141563
## 1838 12 40.894202 52.63749934
## 1839 15 36.899461 72.86735767
## 1840 12 26.307596 117.75840077
## 1841 23 39.590846 59.43646186
## 1842 26 45.325921 28.08040116
## 1843 36 44.851096 30.81788309
## 1844 28 44.402829 33.37882787
## 1845 29 43.093672 40.72774908
## 1846 46 43.328743 39.42247837
## 1847 55 43.099143 40.69744605
## 1848 54 41.730190 48.17530413
## 1849 67 43.185576 40.21818562
## 1850 119 38.349039 65.73540369
## 1851 196 32.308275 93.88582485
## 1852 232 25.776752 119.67395711
## 1853 223 22.412577 131.07171893
## 1854 236 17.025156 146.65474480
## 1855 268 12.259274 157.70026224
## 1856 258 10.398474 161.31474300
## 1857 265 9.246605 163.35569496
## 1858 278 8.431437 164.70927479
## 1859 266 8.548808 164.51901692
## 1860 238 10.467904 161.18692049
## 1861 212 15.553057 150.34104543
## 1862 167 28.486357 109.56206841
## 1863 143 31.224658 98.49846323
## 1864 108 30.124289 103.04634806
## 1865 94 28.826451 108.23415806
## 1866 126 29.362588 106.11419408
## 1867 111 29.298099 106.37091719
## 1868 90 30.962111 99.59603809
## 1869 95 32.156791 94.53864249
## 1870 91 32.444889 93.29486084
## 1871 98 31.456757 97.52167639
## 1872 103 30.601923 101.08910183
## 1873 107 31.262386 98.34010007
## 1874 98 30.185036 102.79885334
## 1875 111 30.633360 100.95937286
## 1876 122 29.411794 105.91799904
## 1877 107 30.798592 100.27568503
## 1878 113 32.675160 92.29396897
## 1879 103 31.914870 95.57580591
## 1880 99 32.868747 91.44788697
## 1881 117 32.334299 93.77340950
## 1882 154 33.085287 90.49645523
## 1883 177 33.528815 88.53111217
## 1884 162 33.640035 88.03478822
## 1885 176 35.204820 80.90334611
## 1886 208 32.726575 92.06967132
## 1887 181 32.464468 93.20999013
## 1888 193 33.484322 88.72927244
## 1889 207 31.733981 96.34698630
## 1890 196 32.866627 91.45717540
## 1891 197 32.235106 94.20146733
## 1892 194 33.245944 89.78713235
## 1893 199 30.728763 100.56499755
## 1894 206 31.336502 98.02852993
## 1895 214 28.023936 111.34659776
## 1896 218 26.240720 118.00147907
## 1897 197 31.765814 96.21154040
## 1898 219 29.346756 106.17726441
## 1899 183 33.425242 88.99205360
## 1900 189 34.339682 84.88044706
## 1901 161 35.948150 77.41851064
## 1902 156 34.114119 85.90344409
## 1903 127 35.303500 80.44432184
## 1904 118 33.728612 87.63850579
## 1905 105 36.744329 73.61651342
## 1906 92 37.316426 70.84026027
## 1907 92 38.327365 65.84379315
## 1908 86 36.350765 75.50487179
## 1909 71 38.849834 63.21618123
## 1910 67 39.517896 59.81131912
## 1911 75 38.807262 63.43144321
## 1912 66 39.055788 62.17190136
## 1913 50 39.193709 61.46989149
## 1914 61 40.842215 52.91237323
## 1915 64 40.204832 56.25756552
## 1916 60 40.751864 53.38936100
## 1917 72 40.286463 55.83170882
## 1918 98 40.809108 53.08726272
## 1919 72 39.167097 61.60551021
## 1920 50 38.966954 62.62291710
## 1921 10 44.802940 31.09409093
## 1922 10 38.441930 65.27026772
## 1923 13 43.932600 36.04077937
## 1924 4 48.348314 10.05712177
## 1925 13 45.200892 28.80370174
## 1926 12 40.178241 56.39612219
## 1927 13 43.920603 36.10837027
## 1928 9 42.018774 46.61657967
## 1929 6 35.080517 81.47998835
## 1930 5 40.000369 57.32090711
## 1931 8 46.170735 23.14672203
## 1932 7 45.489573 27.13099289
## 1933 8 50.594514 -4.00756768
## 1934 13 43.693196 37.38642613
## 1935 11 35.611306 79.00543582
## 1936 11 36.796672 73.36404667
## 1937 18 40.582801 54.27941505
## 1938 26 41.404920 49.92088327
## 1939 24 40.782546 53.22748644
## 1940 21 44.187605 34.60031391
## 1941 27 45.694157 25.93985423
## 1942 36 44.138683 34.87723452
## 1943 44 42.787529 42.41827701
## 1944 60 43.723515 37.21636414
## 1945 79 42.558850 43.67412524
## 1946 119 37.087292 71.95664285
## 1947 134 33.915513 86.79941574
## 1948 130 33.868725 87.00984192
## 1949 107 31.950790 95.42222758
## 1950 84 32.877558 91.40927443
## 1951 75 29.496963 105.57775668
## 1952 78 29.710317 104.72182258
## 1953 102 31.518279 97.26173572
## 1954 110 29.236945 106.61392764
## 1955 122 30.045135 103.36820850
## 1956 123 31.865080 95.78844652
## 1957 131 32.974224 90.98510684
## 1958 116 30.224827 102.63651031
## 1959 131 30.218672 102.66163387
## 1960 107 30.893140 99.88307587
## 1961 78 30.502813 101.49735734
## 1962 30 29.851737 104.15163594
## 1963 81 30.608359 101.06255015
## 1964 45 29.157398 106.92938992
## 1965 10 25.669989 120.05535715
## 1966 40 33.499165 88.66319258
## 1967 62 32.205628 94.32846185
## 1968 90 30.624037 100.99785764
## 1969 91 30.740604 100.51597671
## 1970 79 31.064106 99.17057590
## 1971 75 29.225359 106.65991816
## 1972 91 30.550132 101.30257762
## 1973 68 32.068974 94.91589563
## 1974 67 32.459939 93.22962474
## 1975 60 31.554965 97.10653137
## 1976 67 31.253934 98.37559211
## 1977 85 31.988027 95.26286506
## 1978 78 32.904675 91.29039331
## 1979 81 36.683000 73.91192927
## 1980 77 35.167322 81.07748504
## 1981 80 34.639871 83.51005738
## 1982 72 35.587109 79.11893436
## 1983 84 33.609061 88.17314986
## 1984 123 36.105579 76.67243302
## 1985 117 34.634798 83.53330119
## 1986 120 36.193879 76.25274066
## 1987 136 32.876305 91.41476861
## 1988 144 34.957892 82.04713346
## 1989 186 32.413318 93.43161627
## 1990 148 30.630896 100.96954605
## 1991 147 32.768137 91.88813664
## 1992 149 34.746836 83.01928525
## 1993 136 33.209814 89.94690613
## 1994 128 34.401202 84.60043497
## 1995 140 33.938475 86.69605478
## 1996 93 35.945988 77.42873559
## 1997 117 37.681108 69.05119896
## 1998 102 37.490637 69.98749209
## 1999 109 37.487217 70.00426712
## 2000 59 36.245080 76.00897216
## 2001 46 36.524157 74.67508441
## 2002 73 40.948112 52.35213479
## 2003 53 41.943112 47.02616365
## 2004 51 42.442939 44.30841933
## 2005 49 39.612761 59.32373325
## 2006 61 37.827574 68.32842197
## 2007 55 40.210112 56.23004404
## 2008 39 41.708978 48.28950874
## 2009 46 42.446561 44.28862009
## 2010 47 42.475428 44.13078398
## 2011 48 42.081408 46.27702411
## 2012 34 41.387123 50.01604447
## 2013 31 39.458963 60.11371325
## 2014 32 40.657227 53.88798987
## 2015 51 42.464735 44.18926302
## 2016 21 44.810727 31.04944321
## 2017 20 46.067558 23.75360921
## 2018 23 43.458214 38.70089849
## 2019 14 47.464298 15.43575474
## 2020 13 36.207916 76.18593662
## 2021 21 32.486520 93.11435174
## 2022 21 37.204042 71.38855648
## 2023 15 43.210453 40.08008584
## 2024 24 46.569341 20.79082096
## 2025 13 42.756332 42.58995300
## 2026 9 40.585301 54.26627564
## 2027 13 35.884691 77.71845961
## 2028 13 40.505002 54.68790540
## 2029 20 39.437381 60.22435078
## 2030 12 36.322725 75.63874452
## 2031 19 40.580944 54.28917366
## 2032 14 42.027264 46.57057917
## 2033 18 41.180500 51.11825489
## 2034 28 41.895965 47.28105712
## 2035 27 41.023056 51.95488492
## 2036 18 45.689132 25.96917310
## 2037 29 43.110276 40.63576125
## 2038 42 42.343618 44.85071469
## 2039 54 40.368830 55.40124353
## 2040 57 40.862048 52.80754684
## 2041 68 39.503510 59.88517028
## 2042 129 36.406767 75.23724201
## 2043 141 31.596060 96.93249068
## 2044 162 25.695013 119.96607586
## 2045 160 26.234912 118.02256531
## 2046 162 22.968285 129.27735483
## 2047 168 20.253524 137.71138606
## 2048 127 24.321873 124.76033280
## 2049 132 26.089636 118.54877151
## 2050 134 26.890870 115.61685639
## 2051 132 24.519750 124.08262074
## 2052 118 26.216738 118.08852628
## 2053 82 30.081572 103.22013342
## 2054 110 32.652467 92.39287469
## 2055 130 31.949959 95.42578161
## 2056 118 33.081559 90.51288236
## 2057 121 32.015301 95.14604371
## 2058 128 32.223977 94.24942532
## 2059 108 33.041077 90.69113697
## 2060 96 32.987785 90.92551424
## 2061 79 32.077096 94.88103999
## 2062 100 33.849959 87.09417269
## 2063 105 33.817268 87.24097855
## 2064 88 34.512486 84.09282558
## 2065 98 32.943839 91.11855079
## 2066 95 33.991077 86.45905106
## 2067 97 31.715797 96.42430350
## 2068 110 31.589197 96.96157056
## 2069 106 32.037380 95.05140852
## 2070 100 32.248881 94.14208899
## 2071 123 32.451717 93.26526686
## 2072 102 33.810354 87.27201088
## 2073 92 34.621210 83.59554519
## 2074 92 34.750091 83.00433072
## 2075 101 36.239914 76.03357954
## 2076 113 36.541030 74.59415192
## 2077 121 36.057538 76.90040510
## 2078 121 39.142209 61.73227477
## 2079 122 34.914714 82.24642645
## 2080 132 35.623549 78.94798319
## 2081 167 32.501348 93.05001067
## 2082 131 36.289406 75.79770131
## 2083 149 34.197155 85.52752028
## 2084 194 35.463129 79.69944999
## 2085 187 30.172811 102.84869542
## 2086 162 30.711388 100.63689613
## 2087 150 34.501869 84.14131360
## 2088 145 35.152907 81.14438321
## 2089 123 35.232906 80.77281270
## 2090 134 33.254340 89.74998420
## 2091 152 35.226401 80.80305070
## 2092 115 36.008497 77.13284798
## 2093 147 34.456963 84.34626081
## 2094 119 35.677342 78.69534020
## 2095 109 37.064999 72.06494337
## 2096 102 36.925000 72.74376550
## 2097 69 36.782857 73.43071140
## 2098 68 36.397886 75.27970746
## 2099 61 37.774073 68.59272208
## 2100 72 38.725131 63.84614907
## 2101 68 38.776181 63.58846985
## 2102 78 40.396330 55.25735351
## 2103 59 41.947333 47.00333129
## 2104 59 38.362668 65.66722109
## 2105 65 39.293487 60.96068516
## 2106 65 39.490816 59.95031791
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## 24537 87 34.236632 85.34852549
## 24538 80 28.045067 111.26557987
## 24539 92 28.164341 110.80731921
## 24540 93 36.118158 76.61269941
## 24541 95 38.765369 63.64307077
## 24542 107 37.957604 67.68472475
## 24543 120 38.075960 67.09714925
## 24544 141 36.008081 77.13481993
## 24545 126 35.190216 80.97118172
## 24546 124 37.683223 69.04077913
## 24547 118 38.287216 66.04443046
## 24548 103 40.594672 54.21702504
## 24549 106 42.073008 46.32259131
## 24550 118 40.527679 54.56890825
## 24551 104 39.597237 59.40359358
## 24552 90 41.028398 51.92654361
## 24553 97 40.558762 54.40570578
## 24554 122 38.746245 63.73961081
## 24555 96 40.447137 54.99128984
## 24556 67 42.305008 45.06122674
## 24557 76 38.904250 62.94073600
## 24558 82 40.355898 55.46888093
## 24559 71 41.247534 50.76119749
## 24560 52 40.938153 52.40487665
## 24561 49 41.025012 51.94450544
## 24562 63 41.976109 46.84761939
## 24563 58 38.975211 62.58103595
## 24564 53 38.795863 63.48904746
## 24565 50 41.158356 51.23609405
## 24566 41 42.087240 46.24538995
## 24567 50 42.953042 41.50563012
## 24568 40 44.254088 34.22355091
## 24569 32 43.787300 36.85825677
## 24570 45 42.141619 45.95019499
## 24571 36 40.647907 53.93704136
## 24572 39 39.422406 60.30109441
## 24573 31 39.160508 61.63908011
## 24574 31 40.092920 56.84016719
## 24575 28 40.624425 54.06057732
## 24576 22 44.293727 33.99868087
## 24577 17 46.600564 20.60552188
## 24578 14 43.331424 39.40755858
## 24579 19 43.640327 37.68271280
## 24580 10 44.428246 33.23422616
## 24581 20 45.327022 28.07402486
## 24582 13 45.043572 29.71129007
## 24583 10 43.077041 40.81985812
## 24584 10 43.455542 38.71581102
## 24585 7 45.621902 26.36108637
## 24586 4 41.903291 47.24146592
## 24587 7 45.211918 28.73998805
## 24588 4 43.044133 41.00202873
## 24589 3 48.917986 6.54416486
## 24590 5 40.132591 56.63380604
## 24591 3 45.161018 29.03400295
## 24592 7 46.340327 22.14657607
## 24593 2 59.238223 -63.45997281
## 24594 3 39.302475 60.91476222
## 24595 2 36.316947 75.66631864
## 24596 6 42.136350 45.97880836
## 24597 3 44.189265 34.59090858
## 24598 2 41.094380 51.57623027
## 24599 3 43.744032 37.10122903
## 24600 2 58.648948 -59.13814980
## 24601 6 47.120351 17.50452713
## 24602 12 47.583668 14.71464181
## 24603 16 45.669585 26.08317067
## 24604 27 45.228499 28.64414831
## 24605 23 46.151127 23.26215171
## 24606 18 44.346501 33.69901808
## 24607 29 47.792896 13.44679495
## 24608 30 46.444152 21.53267053
## 24609 20 43.988460 35.72586863
## 24610 30 44.783434 31.20589675
## 24611 27 46.762621 19.64198780
## 24612 26 49.154091 5.07742336
## 24613 20 44.832297 30.92574415
## 24614 30 44.366714 33.58415980
## 24615 32 42.486335 44.07112326
## 24616 55 41.993145 46.75539026
## 24617 41 42.095042 46.20305744
## 24618 36 43.852548 36.49146054
## 24619 45 42.905846 41.76618674
## 24620 20 42.231283 45.46272534
## 24621 46 41.095089 51.57246105
## 24622 62 41.915264 47.17674945
## 24623 69 40.365890 55.41662578
## 24624 84 40.368799 55.40140819
## 24625 69 42.942606 41.56326695
## 24626 91 40.141703 56.58638207
## 24627 78 40.205322 56.25500858
## 24628 75 40.087027 56.87080861
## 24629 77 40.032473 57.15425906
## 24630 77 39.472404 60.04477780
## 24631 58 44.254166 34.22311148
## 24632 66 42.584684 43.53254869
## 24633 55 43.480799 38.57483003
## 24634 51 45.964427 24.35901413
## 24635 56 42.501708 43.98700829
## 24636 54 45.314595 28.14600091
## 24637 55 45.567327 26.67884959
## 24638 53 44.691598 31.73170135
## 24639 61 44.136886 34.88739729
## 24640 67 41.700969 48.33261397
## 24641 66 41.580513 48.98004440
## 24642 77 41.786735 47.87063321
## 24643 84 41.523996 49.28324773
## 24644 85 42.435130 44.35109821
## 24645 83 42.134699 45.98777709
## 24646 89 41.312510 50.41461798
## 24647 88 41.039802 51.86603271
## 24648 98 41.803594 47.77972083
## 24649 82 40.556167 54.41933717
## 24650 89 40.572152 54.33536985
## 24651 88 43.281281 39.68652433
## 24652 85 42.128709 46.02030550
## 24653 92 41.691810 48.38189940
## 24654 96 42.650433 43.17188673
## 24655 92 41.411671 49.88477341
## 24656 83 42.561082 43.66189447
## 24657 61 43.828368 36.62744539
## 24658 75 41.955645 46.95836269
## 24659 65 40.442674 55.01467557
## 24660 58 38.875993 63.08381173
## 24661 57 41.048120 51.82188746
## 24662 59 39.871258 57.98992954
## 24663 52 41.033047 51.90187894
## 24664 35 41.174127 51.15217432
## 24665 36 46.406372 21.75619974
## 24666 37 44.437832 33.17967609
## 24667 43 43.094938 40.72073581
## 24668 35 41.646948 48.62317054
## 24669 39 46.091349 23.61377376
## 24670 29 44.400763 33.39057927
## 24671 33 43.597694 37.92141144
## 24672 16 45.167742 28.99518072
## 24673 18 47.109692 17.56842258
## 24674 18 44.851799 30.81385390
## 24675 19 45.735384 25.69924833
## 24676 17 46.612417 20.53514563
## 24677 10 42.052186 46.43549991
## 24678 8 47.301987 16.41369577
## 24679 8 41.149427 51.28359339
## 24680 9 46.656395 20.27390548
## 24681 5 48.849289 6.96974153
## 24682 4 52.030527 -13.29860880
## 24683 3 52.771157 -18.18177897
## 24684 5 52.309376 -15.12984347
## 24685 8 49.570493 2.47524605
## 24686 8 44.975326 30.10413587
## 24687 5 53.785333 -24.96927642
## 24688 9 44.490582 32.87928543
## 24689 12 46.472703 21.36363950
## 24690 11 46.313348 22.30589523
## 24691 6 44.979083 30.08252367
## 24692 7 43.066977 40.87558469
## 24693 10 41.329947 50.32153067
## 24694 19 45.008082 29.91565018
## 24695 20 44.800598 31.10751837
## 24696 21 49.513940 2.82981122
## 24697 19 47.252185 16.71315790
## 24698 30 46.539204 20.96956914
## 24699 49 44.695516 31.70928967
## 24700 38 44.575470 32.39522858
## 24701 38 45.471097 27.23833209
## 24702 58 44.592587 32.29751853
## 24703 71 43.195223 40.16463866
## 24704 63 44.151836 34.80280932
## 24705 62 45.238152 28.58833887
## 24706 87 43.981288 35.76631984
## 24707 89 44.365975 33.58836256
## 24708 73 45.018596 29.85511924
## 24709 26 46.161938 23.19851356
## 24710 1 3.067240 171.73973939
## 24711 1 3.067240 171.73973939
## 24712 0 NA NA
## 24713 2 35.907036 77.61289585
## 24714 2 35.907036 77.61289585
## 24715 0 NA NA
## 24716 0 NA NA
## 24717 1 44.646630 31.98881587
## 24718 7 37.995638 67.49607577
## 24719 44 39.632747 59.22087538
## 24720 56 37.355620 70.64870143
## 24721 65 36.127382 76.56888388
## 24722 64 33.387636 89.15911870
## 24723 80 33.620865 88.12043423
## 24724 75 34.945452 82.10457438
## 24725 63 34.410648 84.55740074
## 24726 64 34.096469 85.98325264
## 24727 80 33.811262 87.26793555
## 24728 93 35.836367 77.94656322
## 24729 66 35.503832 79.50905734
## 24730 77 33.970111 86.55355542
## 24731 114 33.296030 89.56539679
## 24732 115 36.394710 75.29488938
## 24733 96 38.815670 63.38894295
## 24734 90 38.859437 63.16759709
## 24735 89 37.078886 71.99748327
## 24736 94 36.360721 75.45732010
## 24737 97 39.440600 60.20785485
## 24738 86 38.257348 66.19357512
## 24739 91 36.774402 73.47149835
## 24740 91 33.509153 88.61871170
## 24741 111 30.215087 102.67626595
## 24742 121 29.785046 104.42080809
## 24743 129 34.775368 82.88815936
## 24744 141 36.808330 73.30777286
## 24745 149 37.478526 70.04688377
## 24746 144 39.146395 61.71095995
## 24747 109 40.500117 54.71353129
## 24748 95 38.045695 67.24754824
## 24749 114 40.028486 57.17496029
## 24750 103 41.395520 49.97115001
## 24751 103 42.746775 42.64252652
## 24752 95 41.068212 51.71522115
## 24753 98 41.453866 49.65897784
## 24754 88 41.531674 49.24207371
## 24755 80 41.935633 47.06661243
## 24756 90 44.378221 33.51875551
## 24757 81 42.429127 44.38390054
## 24758 75 42.141826 45.94906946
## 24759 83 40.845916 52.89281577
## 24760 63 40.339621 55.55398309
## 24761 72 41.428071 49.79703871
## 24762 76 42.783094 42.44269057
## 24763 54 42.245865 45.38335786
## 24764 45 43.177684 40.26197904
## 24765 48 43.032520 41.06628005
## 24766 45 43.592981 37.94778586
## 24767 42 43.803941 36.76475476
## 24768 36 40.456895 54.94015744
## 24769 33 39.370360 60.56760506
## 24770 37 38.714942 63.89754101
## 24771 31 38.375567 65.60266986
## 24772 38 41.704837 48.31179601
## 24773 37 41.196551 51.03280979
## 24774 37 43.119507 40.58460534
## 24775 24 50.478713 -3.26850370
## 24776 32 46.855204 19.09018566
## 24777 36 44.858505 30.77536924
## 24778 24 44.033573 35.47128510
## 24779 13 40.498912 54.71985527
## 24780 28 48.983832 6.13574845
## 24781 19 41.637694 48.67290741
## 24782 26 43.082292 40.79078262
## 24783 26 43.122920 40.56568812
## 24784 27 46.826575 19.26092468
## 24785 24 48.135209 11.36181185
## 24786 34 46.248568 22.68811560
## 24787 29 51.133922 -7.47017090
## 24788 25 47.590309 14.67447370
## 24789 34 48.002375 12.17246369
## 24790 40 45.642804 26.23929067
## 24791 35 45.543733 26.81612267
## 24792 42 44.446136 33.13240752
## 24793 46 42.939495 41.58044528
## 24794 75 41.917940 47.16228354
## 24795 102 40.480024 54.81891239
## 24796 103 41.102230 51.53451830
## 24797 117 40.185869 56.35638448
## 24798 113 37.763223 68.64627781
## 24799 123 38.750969 63.71576697
## 24800 119 40.343896 55.53163717
## 24801 142 39.343823 60.70337358
## 24802 137 36.526734 74.66272369
## 24803 127 38.442311 65.26835728
## 24804 91 37.734252 68.78922330
## 24805 29 33.732804 87.61972667
## 24806 2 11.304769 159.60330316
## 24807 0 NA NA
## 24808 0 NA NA
## 24809 0 NA NA
## 24810 0 NA NA
## 24811 0 NA NA
## 24812 0 NA NA
## 24813 4 32.837507 91.58470940
## 24814 58 30.477388 101.60190933
## 24815 98 28.510689 109.46749872
## 24816 112 27.258813 114.24610689
## 24817 125 24.826294 123.02398091
## 24818 123 24.957370 122.56806522
## 24819 123 20.681612 136.43685535
## 24820 117 20.428915 137.19170939
## 24821 135 22.610257 130.43742430
## 24822 122 26.129273 118.40544047
## 24823 118 28.847300 108.15232732
## 24824 120 29.774811 104.46207184
## 24825 102 28.534677 109.37420099
## 24826 105 29.990078 103.59166884
## 24827 132 32.036477 95.05528011
## 24828 112 35.622831 78.95135167
## 24829 114 39.191183 61.48276583
## 24830 127 37.936038 67.79161720
## 24831 136 36.305734 75.71981613
## 24832 142 37.273901 71.04789934
## 24833 134 35.686910 78.65037091
## 24834 151 35.510938 79.47580112
## 24835 134 35.840736 77.92594752
## 24836 126 37.750300 68.71005682
## 24837 128 37.668065 69.11544221
## 24838 108 39.540676 59.69432657
## 24839 127 36.665140 73.99788059
## 24840 116 38.935669 62.78154226
## 24841 115 38.605556 64.44855893
## 24842 121 37.793671 68.49594056
## 24843 123 38.466783 65.14565490
## 24844 103 38.336120 65.80001632
## 24845 100 38.725644 63.84356276
## 24846 95 40.136716 56.61233977
## 24847 102 39.390520 60.46440563
## 24848 66 36.433762 75.10810361
## 24849 72 37.131046 71.74392270
## 24850 78 39.088689 62.00463142
## 24851 59 39.973390 57.46086042
## 24852 63 41.536326 49.21712919
## 24853 60 39.937151 57.64872521
## 24854 59 42.477570 44.11906975
## 24855 61 41.005516 52.04791374
## 24856 56 43.575791 38.04395962
## 24857 44 44.610228 32.19678944
## 24858 60 42.447001 44.28621387
## 24859 47 43.430784 38.85393275
## 24860 48 41.170389 51.17206933
## 24861 40 40.851464 52.86349084
## 24862 33 42.625483 43.30880435
## 24863 37 42.345708 44.83931264
## 24864 42 42.674282 43.04094074
## 24865 31 41.081266 51.64589476
## 24866 38 41.309150 50.43255184
## 24867 24 43.020349 41.13360988
## 24868 28 46.111403 23.49586127
## 24869 22 46.153145 23.25027217
## 24870 16 47.322542 16.29001345
## 24871 13 45.930044 24.56058451
## 24872 18 45.978539 24.27624419
## 24873 14 41.374911 50.08132096
## 24874 18 33.723891 87.65964657
## 24875 22 39.852253 58.08825186
## 24876 22 45.978520 24.27635560
## 24877 13 45.188858 28.87322824
## 24878 12 46.426787 21.63543213
## 24879 21 45.217522 28.70760155
## 24880 22 44.201474 34.52175783
## 24881 11 37.557894 69.65734434
## 24882 29 45.690297 25.96237291
## 24883 22 42.705824 42.86766395
## 24884 21 45.007532 29.91881384
## 24885 26 48.108894 11.52256511
## 24886 29 48.372538 9.90848966
## 24887 26 44.943733 30.28581362
## 24888 41 44.259195 34.19459381
## 24889 44 45.511708 27.00234868
## 24890 64 45.155011 29.06868054
## 24891 91 41.958143 46.94484405
## 24892 93 39.786400 58.42861874
## 24893 103 41.258531 50.70257371
## 24894 89 40.338822 55.55816263
## 24895 112 39.007503 62.41716011
## 24896 97 37.579536 69.55100256
## 24897 124 38.505685 64.95045679
## 24898 123 38.010437 67.42262969
## 24899 129 39.522529 59.78753290
## 24900 108 40.235735 56.09643825
## 24901 115 38.894354 62.99085060
## 24902 119 37.256785 71.13141224
## 24903 43 36.259330 75.94107477
## 24904 21 33.018456 90.79066420
## 24905 63 34.952847 82.07042964
## 24906 51 30.437705 101.76494735
## 24907 61 33.672514 87.88958222
## 24908 91 34.804208 82.75552169
## 24909 77 33.851465 87.08740350
## 24910 111 31.435741 97.61037436
## 24911 107 31.485695 97.39946435
## 24912 116 32.324519 93.81566615
## 24913 109 28.250151 110.47663552
## 24914 98 27.628246 112.85438152
## 24915 132 25.565225 120.42836201
## 24916 143 25.509528 120.62616151
## 24917 134 25.024163 122.33499454
## 24918 130 26.082103 118.57599198
## 24919 132 31.794433 96.08967639
## 24920 119 31.937625 95.47853182
## 24921 106 33.260974 89.72062243
## 24922 135 32.877626 91.40897983
## 24923 144 33.295350 89.56841175
## 24924 134 34.623602 83.58458747
## 24925 144 36.864993 73.03404583
## 24926 129 35.993872 77.20211701
## 24927 159 33.916599 86.79453043
## 24928 159 34.796946 82.78892870
## 24929 148 36.136251 76.52674545
## 24930 140 35.543927 79.32132642
## 24931 145 34.787258 82.83348874
## 24932 151 35.677361 78.69525185
## 24933 140 34.069905 86.10329591
## 24934 135 34.940581 82.12706175
## 24935 122 34.532016 84.00360103
## 24936 134 37.244585 71.19092118
## 24937 136 37.909985 67.92067685
## 24938 132 38.345250 65.75435446
## 24939 123 36.821677 73.24332991
## 24940 127 38.614306 64.40452973
## 24941 112 38.274151 66.10968535
## 24942 108 39.322415 60.81284401
## 24943 110 38.551562 64.72004379
## 24944 96 39.615000 59.31221253
## 24945 72 38.364635 65.65737857
## 24946 60 40.610655 54.13299465
## 24947 66 40.794946 53.16203525
## 24948 65 41.035646 51.88808716
## 24949 67 40.321635 55.64798979
## 24950 55 38.582626 64.56389260
## 24951 55 40.592548 54.22818755
## 24952 42 39.089995 61.99798692
## 24953 54 40.528741 54.56333707
## 24954 52 42.557239 43.68295000
## 24955 40 44.168171 34.71034865
## 24956 42 44.510789 32.76413417
## 24957 50 40.308121 55.71859312
## 24958 43 38.627746 64.33688815
## 24959 35 39.751752 58.60750405
## 24960 40 41.171700 51.16509326
## 24961 0 NA NAp_quad_fit <-
ggplot(quad_fit_plot) +
# geom_point(
# aes(x = mean_speed, y = flow)
# ) +
geom_line(
aes(x = mean_speed, y = quad_eq)
)
p_quad_fit## Warning: Removed 5333 row(s) containing missing values (geom_path).
quad_fit_typical <- lm(formula = flow ~ poly(mean_speed, 2, raw = TRUE), data = flows_23_typical)
summary(quad_fit_typical)##
## Call:
## lm(formula = flow ~ poly(mean_speed, 2, raw = TRUE), data = flows_23_typical)
##
## Residuals:
## Min 1Q Median 3Q Max
## -195.74 -31.93 -2.26 30.59 174.56
##
## Coefficients:
## Estimate Std. Error t value
## (Intercept) 198.915415 3.319199 59.929
## poly(mean_speed, 2, raw = TRUE)1 -0.505514 0.233091 -2.169
## poly(mean_speed, 2, raw = TRUE)2 -0.072790 0.003946 -18.446
## Pr(>|t|)
## (Intercept) <0.0000000000000002 ***
## poly(mean_speed, 2, raw = TRUE)1 0.0301 *
## poly(mean_speed, 2, raw = TRUE)2 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 56.45 on 13397 degrees of freedom
## (616 observations deleted due to missingness)
## Multiple R-squared: 0.4068, Adjusted R-squared: 0.4067
## F-statistic: 4594 on 2 and 13397 DF, p-value: < 0.00000000000000022quad_fit_atypical <- lm(formula = flow ~ poly(mean_speed, 2, raw = TRUE), data = flows_23_atypical)
summary(quad_fit_atypical)##
## Call:
## lm(formula = flow ~ poly(mean_speed, 2, raw = TRUE), data = flows_23_atypical)
##
## Residuals:
## Min 1Q Median 3Q Max
## -71.375 -22.084 0.412 19.210 255.114
##
## Coefficients:
## Estimate Std. Error t value
## (Intercept) 8.042650 3.984869 2.018
## poly(mean_speed, 2, raw = TRUE)1 5.131332 0.250497 20.485
## poly(mean_speed, 2, raw = TRUE)2 -0.102308 0.003917 -26.116
## Pr(>|t|)
## (Intercept) 0.0436 *
## poly(mean_speed, 2, raw = TRUE)1 <0.0000000000000002 ***
## poly(mean_speed, 2, raw = TRUE)2 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 34.39 on 6225 degrees of freedom
## (4717 observations deleted due to missingness)
## Multiple R-squared: 0.1678, Adjusted R-squared: 0.1676
## F-statistic: 627.8 on 2 and 6225 DF, p-value: < 0.00000000000000022# Pearson Correlation test entire for entire traffics
cor.test(flows_23_weekday$flow, flows_23_weekday$mean_speed, method = "pearson")##
## Pearson's product-moment correlation
##
## data: flows_23_weekday$flow and flows_23_weekday$mean_speed
## t = -94.53, df = 19626, p-value < 0.00000000000000022
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.5688786 -0.5496514
## sample estimates:
## cor
## -0.5593403# Pearson Correlation test entire for typical traffics
cor.test(flows_23_typical$flow, flows_23_typical$mean_speed, method = "pearson")##
## Pearson's product-moment correlation
##
## data: flows_23_typical$flow and flows_23_typical$mean_speed
## t = -92.894, df = 13398, p-value < 0.00000000000000022
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.6360924 -0.6154927
## sample estimates:
## cor
## -0.6259017# Pearson Correlation test entire for atypical traffics
cor.test(flows_23_atypical$flow, flows_23_atypical$mean_speed, method = "pearson")##
## Pearson's product-moment correlation
##
## data: flows_23_atypical$flow and flows_23_atypical$mean_speed
## t = -22.736, df = 6226, p-value < 0.00000000000000022
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.299654 -0.253787
## sample estimates:
## cor
## -0.2768782flows_23_2jan <-
flow_with_expected %>%
filter(as_date(t) == "2018-01-02") %>%
mutate(quantile25 = quantile(flow, 0.25)) %>%
mutate(start = hms::as_hms(t)) %>%
mutate(end = hms::as_hms(start + hms::as_hms("00:15:00"))) %>%
mutate(flow_diff = abs(flow - median_flow)) %>%
mutate(condition = ifelse(flow_diff > quantile25, "ABNORMAL", "NORMAL"))p_clust_2jan <-
ggplot(flows_23_2jan) +
geom_line(
aes(
x = start,
y = flow
)
) +
geom_rect(
aes(
xmin = start,
xmax = end,
fill = condition
),
ymin = -Inf,
ymax = Inf,
alpha = 0.5
) +
scale_fill_manual(values = c("grey", NA)) +
xlab("Time") +
ylab("Flow") +
theme_bw()
p_clust_2jan
sum(flows_23_2jan$condition == "ABNORMAL")/length(flows_23_2jan$condition)## [1] 0.3645833nrow(flows_23_weekday[flows_23_weekday$flow == 0,])/nrow(flows_23_weekday[flows_23_weekday$flow != 0,])*100## [1] 27.17037expected_typical <-
flows_23_labelled %>%
filter(cluster_label == "typical") %>%
mutate(time = hms::as_hms(t)) %>%
group_by(o, d, time) %>%
summarise(
median_typical = median(flow)
)flow_with_expected <- inner_join(flow_with_expected, expected_typical, by = c("o", "d", "time"))flows_23_2jan_typ <-
flow_with_expected %>%
filter(as_date(t) == "2018-01-02") %>%
mutate(quantile25 = quantile(flow, 0.25)) %>%
mutate(start = hms::as_hms(t)) %>%
mutate(end = hms::as_hms(start + hms::as_hms("00:15:00"))) %>%
mutate(flow_diff = abs(flow - median_typical)) %>%
mutate(condition = ifelse(flow_diff > quantile25, "ABNORMAL", "NORMAL"))p_clust_2jan_typ <-
ggplot(flows_23_2jan_typ) +
geom_line(
aes(
x = start,
y = flow
)
) +
geom_rect(
aes(
xmin = start,
xmax = end,
fill = condition
),
ymin = -Inf,
ymax = Inf,
alpha = 0.5
) +
scale_fill_manual(values = c("grey", NA)) +
xlab("Time") +
ylab("Flow") +
theme_bw()
p_clust_2jan_typ
sum(flows_23_2jan_typ$condition == "ABNORMAL")/length(flows_23_2jan_typ$condition)## [1] 0.3333333flows_23_10jul <-
flow_with_expected %>%
filter(as_date(t) == "2018-07-10") %>%
mutate(quantile25 = quantile(flow, 0.25)) %>%
mutate(start = hms::as_hms(t)) %>%
mutate(end = hms::as_hms(start + hms::as_hms("00:15:00"))) %>%
mutate(flow_diff = abs(flow - median_flow)) %>%
mutate(condition = ifelse(flow_diff > quantile25, "ABNORMAL", "NORMAL"))flows_23_10jul_typ <-
flow_with_expected %>%
filter(as_date(t) == "2018-07-10") %>%
mutate(quantile25 = quantile(flow, 0.25)) %>%
mutate(start = hms::as_hms(t)) %>%
mutate(end = hms::as_hms(start + hms::as_hms("00:15:00"))) %>%
mutate(flow_diff = abs(flow - median_typical)) %>%
mutate(condition = ifelse(flow_diff > quantile25, "ABNORMAL", "NORMAL"))p_clust_10jul <-
ggplot(flows_23_10jul) +
geom_line(
aes(
x = start,
y = flow
)
) +
geom_rect(
aes(
xmin = start,
xmax = end,
fill = condition
),
ymin = -Inf,
ymax = Inf,
alpha = 0.5
) +
scale_fill_manual(values = c("grey", NA)) +
xlab("Time") +
ylab("Flow") +
theme_bw()
p_clust_10jul
sum(flows_23_10jul$condition == "ABNORMAL")/length(flows_23_10jul$condition)## [1] 0.3333333p_clust_10jul_typ <-
ggplot(flows_23_10jul_typ) +
geom_line(
aes(
x = start,
y = flow
)
) +
geom_rect(
aes(
xmin = start,
xmax = end,
fill = condition
),
ymin = -Inf,
ymax = Inf,
alpha = 0.5
) +
scale_fill_manual(values = c("grey", NA)) +
xlab("Time") +
ylab("Flow") +
theme_bw()
p_clust_10jul_typ
sum(flows_23_10jul_typ$condition == "ABNORMAL")/length(flows_23_10jul_typ$condition)## [1] 0.3229167fig1 <- ggarrange(p_clust_2jan, p_clust_2jan_typ,
labels = c("A", "B"),
ncol = 1, nrow = 2)
annotate_figure(fig1,
top = text_grob("Abnormal flow detection on 2 January 2018", color = "Black", face = "bold", size = 12))
fig2 <- ggarrange(p_clust_10jul, p_clust_10jul_typ,
labels = c("A", "B"),
ncol = 1, nrow = 2)
annotate_figure(fig2,
top = text_grob("Abnormal flow detection on 10 July 2018", color = "Black", face = "bold", size = 12))
Atypical Flow Analysis
flows_23_atypical_real <-
flows_23_atypical %>%
filter(flow != 0) flows_23_atypical_real %>%
filter(flow == 1)## # A tibble: 120 x 9
## o d t flow mean_speed dayt month
## <fct> <fct> <dttm> <int> <dbl> <date> <dbl>
## 1 2 3 2018-04-20 13:15:00 1 30.0 2018-04-20 4
## 2 2 3 2018-04-24 06:15:00 1 5.53 2018-04-24 4
## 3 2 3 2018-04-24 08:00:00 1 16.4 2018-04-24 4
## 4 2 3 2018-05-01 07:30:00 1 11.1 2018-05-01 5
## 5 2 3 2018-05-01 07:45:00 1 11.1 2018-05-01 5
## 6 2 3 2018-05-03 06:30:00 1 18.6 2018-05-03 5
## 7 2 3 2018-05-03 07:15:00 1 14.9 2018-05-03 5
## 8 2 3 2018-05-03 07:30:00 1 14.9 2018-05-03 5
## 9 2 3 2018-05-07 07:00:00 1 44.6 2018-05-07 5
## 10 2 3 2018-05-07 08:45:00 1 51.6 2018-05-07 5
## # … with 110 more rows, and 2 more variables: cluster_label <fct>, time <time>flows_23_atypical_real %>%
filter(dayt == "2018-04-24")## # A tibble: 96 x 9
## o d t flow mean_speed dayt month
## <fct> <fct> <dttm> <int> <dbl> <date> <dbl>
## 1 2 3 2018-04-24 00:00:00 29 44.3 2018-04-24 4
## 2 2 3 2018-04-24 00:15:00 20 44.2 2018-04-24 4
## 3 2 3 2018-04-24 00:30:00 13 35.8 2018-04-24 4
## 4 2 3 2018-04-24 00:45:00 13 43.9 2018-04-24 4
## 5 2 3 2018-04-24 01:00:00 7 47.1 2018-04-24 4
## 6 2 3 2018-04-24 01:15:00 13 46.1 2018-04-24 4
## 7 2 3 2018-04-24 01:30:00 13 49.4 2018-04-24 4
## 8 2 3 2018-04-24 01:45:00 12 45.9 2018-04-24 4
## 9 2 3 2018-04-24 02:00:00 10 41.6 2018-04-24 4
## 10 2 3 2018-04-24 02:15:00 10 44.0 2018-04-24 4
## # … with 86 more rows, and 2 more variables: cluster_label <fct>, time <time>